Let `alpha`, `beta (a lt b)` be the roots of the equation `ax^(2)+bx+c=0`. If `lim_(xtoalpha ) (|ax^(2)+bx+c|)/(ax^(2)+bx+c)=1` then

Options

A. `(|a|)/(a)=-1`,
B. `a gt 0`,
C. `(|a|)/(a)=1`,
D. `a lt 0`,

Answer

C

Explanation

`(c )` According to the given condition, we have
`|am^(2)+bm+c|=am^(2)+bm+c`
i.e., `am^(2)+bm+c gt 0`
`implies` if `a lt 0` , then `m` lies in `(alpha,beta)`
and if `a gt 0`, then `m` does not lie in `(alpha,beta)`
Hence, option `(c )` is correct, since
`(|a|)/(a)=1impliesa gt 0` and in that case `m` does not lie in `(alpha,beta)`.